If you NEED a lot of storage, then the S3 is a better option. Otherwise, I think the Nexus 4 is better in every aspect. Me and my wife both have the Nexus 4, we got the S3 for our daughter. I hate trying to do anything on my daughter's phone. The software on the Nexus is just sooooo much better.
My daughter downloads tons of games and stores a lot of music on hers. Her Nexus S ran out of storage and she couldn't even update apps because she didn't have enough storage available. I didn't want to run into that problem again. I would rather her have a 16gb phone and 32 gb SD and not worry about it.
I keep a few games, the occasional movie (downloaded from Xfinity, then removed once I watch it), and stream everything else. I also utilize the cloud. Last month I used 9gb of data, and I'm on pace to double it this month, just to show how much streaming and using the cloud I do.
My wife calls, texts, uses Facebook, and an occasional game is all she uses her phone for.